Y completed lap in 13 min and rest for 2. Both start walking together in same direction.How many minutes will it be until both meet again?
asked Jul 2 in Word Problem Answers by anonymous

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:

To avoid this verification in future, please log in or register.

1 Answer

Number of laps=n. It takes J 11n-1 minutes to do n laps; it takes Y 15n-2 minutes to do n laps. 

In the time it takes Y to complete n laps, J has completed n+1 laps, so 11(n+1)-1=15n-2.

11n+11-1=15n-2; 12=4n so n=3. Therefore the time is 15*3-2=43 minutes (or 11*4-1=43 minutes).

The graph below shows that they meet up after 43 minutes, J having completed 4 laps while Y completes 3.

The more general solution is that J completes n+k laps while Y completes n laps:

11(n+k)-1=15n-2; 4n=11k+1; 4n=(8+3)k+1; n-2k=3k/4+1/4; m=(3k+1)/4 where m is an integer, and n=m+2k.

For m to be an integer the right-hand side must be divisible by 4, so k=4a+1 for integer a; so k=1, 5, 9, etc.

The lowest value for k is 1, so lowest value for m=1, and n=m+2k=1+2=3, making the shortest time 15*3-2=43 minutes.

answered Jul 2 by Rod Top Rated User (495,340 points)
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
80,130 questions
83,948 answers
66,859 users